Re: st: Testing independence of factor variables in a non-linear specification

[Maarten Buis <maartenlbuis@gmail.com>]

On Sun, Jul 10, 2011 at 9:56 PM, Tanuku AP wrote:
> Based on the following snippet, would it be OK to claim that [H0: interaction terms do not matter] null hypothesis cannot be rejected at the 1% and 5% levels?

> *****************
> . probit choice age disabled##income  i.receduc i.sex, nolog
>
> . testparm disabled#income
>            chi2(  4) =    7.89
>          Prob > chi2 =    0.0956
>
> **************

As usual you must be annoyingly exact when describing a test. The null
hypothesis is not "interaction terms do not matter", but "the
coefficients for the interaction terms are all 0". The two are not the
same, especially in non-linear models like -probit-. If you wish to
interpret your coefficients in terms of marginal effects than you can
easily end up with very different conclusions, see:

Edward C. Norton, Hua Wang, Chunrong Ai (2004), "Computing interaction
effects and standard errors in logit and probit models"  The Stata
Journal, 4(2):154-167.

My interpretation of that article (others disagree) is that it
illustrates the limits of usefulness of marginal effects. Marginal
effects are in effect a (linear) model of your (non-linear) probit
model. As all models it is not an exact representation of what it
summarizes. This does not have to be a problem as long as it is a
useful simplification. However, with interaction effect this
"friction" becomes so large that it is no longer useful. Basically,
you'll end up with a "conclusion" that for some individuals the
interaction effect is significantly positive, for other it is
significantly negative, and for the remaining individuals it is
non-significant. What is worse, this variability does not represent an
aspect of the data, but instead is the result of the friction between
the linear model implied by marginal effects and the non-linear model
implied by -probit-.

For that reason I prefer the -logit- model and the interpretation in
terms of odds ratios. You need to put a bit of effort into helping
your audience understand these coefficients, but that is not as hard
as many seem to fear. See for example:
M.L. Buis (2010) "Stata tip 87: Interpretation of interactions in
non-linear models", The Stata Journal, 10(2), pp. 305-308.

Hope this helps,
Maarten

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany


http://www.maartenbuis.nl
--------------------------

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